The reduction of cross-talk within audio signals is of major interest in a plurality of applications. For example, when reproducing binaural audio signals for a listener using loudspeakers, the audio signals to be heard e.g. in the left ear of the listener are usually also heard in the right ear of the listener. This effect is denoted as cross-talk and can be reduced by adding an inverse filter into the audio reproduction chain. Cross-talk reduction can also be referred to as cross-talk cancellation, and can be realized by filtering the audio signals.
An exact inverse filtering is usually not possible and approximations are applied. Because inverse filters are normally unstable, these approximations use a regularization in order to control the gain of the inverse filters and to reduce the dynamic range loss. However, due to ill-conditioning, the inverse filters are sensitive to errors. In other words, small errors in the reproduction chain can result in large errors at a reproduction point, resulting in a narrow sweet spot and undesired coloration as described in Takeuchi, T. and Nelson, P. A., “Optimal source distribution for binaural synthesis over loudspeakers”, Journal ASA 112(6), 2002.
In EP 1 545 154 A2, measurements from loudspeakers to the listener are used in order to determine the inverse filters. This approach, however, suffers from a narrow sweet spot and unwanted coloration due to regularization. Since all frequencies are treated equally in the optimization stage, low and high frequency components are prone to errors due to the ill-conditioning.
In M. R. Bai, G. Y. Shih, C. C. Lee “Comparative study of audio spatializers for dual-loudspeaker mobile phones”, Journal ASA 121(1), 2007, a sub-band division is used in order to lower the complexity of the inverse filter design. In this approach, a quadrature mirror filter (QMF) filter-bank is used in order to implement cross-talk reduction in a multi-rate manner. However, all frequencies are treated equally and the sub-band division is only used to lower the complexity. As a result, high regularization values are applied, resulting in a lowered spatial perception and sound quality.
In US 2013/0163766 A1, a sub-band analysis is employed in order to optimize the choice of regularization values. Because low and high frequency components use large regularization values, spatial perception and sound quality are affected by this approach.